Harry is correct on the wheels. Early red and then black see through spoke wheels have a peened on gear. Around 1935-36 Lionel switched to the die cast wheels as shown in your picture. They have embossed spokes, but are not "see-through". The casting is the same, whether Lionel applied a thick or thin rim to the wheel. Rim's came in nickel plated(earlier) or that blackened color (later).
The replacement ones Olsen used to sell were made by Bowser back in the day. They were not very good and the axle holes were often off center, resulting in egg rolling if you put them on and tried to run it (found out the hard way).
I finally gave up and just bought a junk loco off eBay with a good motor/wheels and swapped out the motors.
The late 261E you have, should have the same motor in it as a 249E, thus a replacement motor (wheel) should be rather easy to find (You'll just need to find ones with the same rim to match). Some people have had luck pulling a wheel off a junker and remounting it on their good locomotive as well, if done cautiously.
